Optimal Dynamic Pricing for Heterogeneous Objects with Quality Uncertainty

Abstract

This paper studies how a seller dynamically changes the prices for heterogeneous objects with uncertain qualities while facing potential buyers that may arrive over time. We illustrate our approach via two applications. In the sponsored search context, Asian search engines adopt a novel buy-it-now option for selling the positions to advertisers, and they bump up the subsequent advertisers to eliminate the unnecessary waste of empty positions. This creates uncertain click-through rates that are endogenously determined as equilibrium outcomes. In the car rental context, the possibility of no-shows provides the rationale to upgrade customers to higher-class cars. This upgrading allows the seller to utilize leftover inventory and subsequently constitutes the source of quality uncertainty. We provide analytical expressions of the optimal dynamic pricing despite the quality uncertainty, the product heterogeneity, and the stochastic demand. Our numerical experiments in the car rental problem indicate that this quality uncertainty and customer speculation lead to fundamentally different managerial implications than the classical capacity and revenue management literature. The upgrading probability and prices can both be non-monotonic in the remaining inventory levels, and they need not exhibit similar patterns. In addition, A higher no-show probability can result in a reduction of high-end car price but an increase of the high-end car price at the same time. We further find that the benefit of upgrading is more pronounced when the quality difference between low-end and high-end cars is substantial.